Is there a max size for saving openEXR multilayer files?
I don't think there is a limit. In my experience EXR Multilayer Feature works really great in Blender. Make sure that:


you have file permissions to write on your drive, 
it is not a compositor issue or 
you are not running out of memory. 


I once rendered an image which needs to be a 30K EXR Multilayer with all possible passes included, file size was about 12gb. Rendering and Saving as EXR works as expected, but finally the image resolution was to high for the current compositor (2.71) so I can't do the compositing in blender. That's why I suggest you to disable all post processing image operations for the rendering process.

For rendering EXRs with Cycles this answer is also helpful. In this post Brecht even mentioned that rendering EXRs is the only way to write and render the image at the same time. With that in mind it even makes sense to render as EXR for large filesize images.